Could taking GABA help with depression?

Not currently. Gaba is an inhibitory neurotransmitter, and as a supplement is sold as a "natural tranquilizer." by itself it doesn't cross the blood-brain barrier. There may be a role in gaba(b) [a form of gaba] in depression, as this receptor system interacts with the serotonergic system & other neurotropic factors. More research needed to define this, though.